1. Field of the Invention
The present invention relates to aspheric-surface processing methods, and more specifically, to an aspheric-surface processing method for quickly cutting an aspheric surface having a large undulation and an aspheric-surface forming method.
This application is based on Japanese Patent Applications Nos. 2003-044362, 2003-139200, 2003-311407 filed on Feb. 21, 2003, May 16, 2003 and Sep. 3, 2003, respectively, the disclosures of which are incorporated herein by reference in their entirety.
2. Description of Related Art
A progressive dioptric lens without a so-called boundary is often used as a presbyopia-corrective eyeglass lens. In recent years, a so-called inner-surface progressive lens having a concave surface close to an eyeball, formed in a curved surface combined with a progressive surface or a progressive toric surface has been proposed. The inner-surface progressive lens has a drastically improved optical performance by reducing waviness and strain which are drawbacks of the progressive dioptric lens.
Japanese Unexaminer Patent Applications Publication No.s 11-309602, 10-175149 and 2002-283204 provide prior-art literature information related to techniques for generating an axis-asymmetric aspheric surface such as a progressive concave surface of such an eyeglass lens. All of the above mentioned publications are incorporated herein by reference for their helpful background information on previous attempts to generate an aspheric surface quickly and accurately.
A tri-axial control, numerically-controlled cutting apparatus for generating an axis-asymmetric aspheric surface continuously positions a turning tool at predetermined positions with an X-axis table, Y-axis table, and work-axis rotating means, serving as a three-axes positioning mechanism. The numerically controlled cutting apparatus generates a configuration of a lens by cutting the lens in accordance with a design configuration of the lens. A general control method of the cutting apparatus lies in that rotational positions of a work are detected by an encoder while the work is being rotated, and the X-axis table, the Y-axis table, and the work-axis rotating means serving as the three-axes positioning mechanism are controlled in synchronization with the rotational positions.
A normal-control processing method serving as a known configuration-generating control method using the numerically-controlled cutting apparatus will be described with reference to FIGS. 8 to 10. FIG. 8 is a schematic view illustrating a work surface of a lens to be processed in accordance with the normal-control processing method, wherein FIG. 8(a) is an elevation view of the lens, and FIG. 8(b) is a sectional view of the lens taken along the line B-B′ indicated in FIG. 8(a). FIG. 9 is a conceptual view illustrating the normal-control processing method. FIG. 10 is a conceptual view illustrating center positions of a turning tool in the X-direction to be processed in accordance with the normal-control processing method.
Numerical data for an NC control of the normal-control processing method will be described using an arbitrary position Qx shown in FIG. 8(a). When a helix extending at a feed pitch P from the periphery to the center of rotation of a round lens is assumed, the numerical data for the NC control of the normal-control processing method is given by three-dimensional coordinated values (θ, Rx, y) indicating a work position of the lens, wherein θ and Rx are a rotational angle and a distance from the center of rotation of the lens (i.e., a radius of the lens), respectively, providing two-dimensional coordinate values of each of intersections between the helix and radial lines extending from the center of rotation of the lens at a predetermined angle, and y (not shown) is a height of each intersection in accordance with the surface configuration in the Y-direction.
A toric surface of the lens is defined as a curved surface having a curve (a base curve) with the minimum curvature of radius, extending along the line A–A′ and another curve (a cross curve) with the maximum curvature of radius, extending along the line B–B′ perpendicular to the line A–A′, both lines illustrated in FIG. 8(a). When a difference in the curvatures of the radius of the base curve and the cross curve is great, as shown in FIG. 8(b), a cross-section of the lens cut along the cross curve has a curved configuration having very thick ends and a thin central part.
A turning tool 325, shown in FIG. 9, performs a reciprocating motion between the thinnest portion and the thickest portion of the lens once every 90-degrees of rotation. That is, the turning tool 325 performs a reciprocating motion in the Y-direction. For example, when the lens rotates by 90 degrees from an A–A′ cross-section to a B–B′ cross-section as shown in FIG. 9, the turning tool 325 moves towards the positive side of the Y-axis, from an arbitrary work position Qn at the thinnest portion to an arbitrary work position Qnm at the thickest portion.
The tip of the turning tool 325 for cutting the lens has a cross-section of an arch-shape (hereinafter, referred to as a curved shape). In accordance with the normal-control processing method, for example, the center of the curved portion of the tip of the turning tool 325 is positioned along a line being normal to the base curve of the lens and extending through the work position Qn of the lens.
More particularly, at the arbitrary work position Qn of the thinnest portion (the base curve of the A–A′ cross-section), a center position Pn of the turning tool 325 is positioned along the line being normal to the base curve of the lens and extending through the work position Qn. At an arbitrary work position Qnm of the thickest portion (the cross curve of the B–B′ cross-section) where the lens is rotated by 90 degrees from the work position Qn, a center position Pnm of the turning tool 325 is positioned along a line being normal to the cross curve and extending through the work position Qnm. The work position Qnm moves towards the center of the lens in the X-axis direction by a quarter of the feed pitch P from the work position Qn. When moving from the work position Qn to the work position Qnm, the turning tool 325 moves towards the positive side of the Y-axis direction by ΔY while moving relative to the work towards the center of the lens in the X-axis direction by Xm.
At an arbitrary work position Qnr of the thinnest portion (the base curve of the A–A′ cross-section) where the lens is further rotated by 90 degrees as shown in FIG. 10, the turning tool 325 moves towards the negative side of the Y-axis direction, not shown. In this case, with respect to the X-axis direction, since an outward speed of the turning tool 325 due to a decrease in depth of the lens is greater than a feed rate of the turning tool 325 towards the center of the lens, the turning tool 325 moves relative to the work towards the periphery of the lens by Xr as shown in FIG. 10.
That is, the cross curve of the B–B′ cross-section serves as a reverse point between positive and negative signs in the moving direction of the turning tool 325; hence, the turning tool 325 moves in the positive and negative directions in an alternating manner with the cross curve of the B–B′ cross-section as a boundary and performs a reciprocating motion in the X-axis and Y-axis directions.
In accordance with the processing method by means of the normal control, as shown in FIGS. 8–10, intersections between the helix and the radial lines provide work positions, and the cutting apparatus is controlled such that the center position of the tip of the turning tool is positioned along a line being normal to a work surface of the work and extending through the work position. That is, in accordance with the processing method by means of the normal control, a turning tool cuts a work while repeatedly moving in the positive and negative directions in an alternating manner, as described above, and depicting a complicated helical path in a zigzag manner.
In accordance with the normal-control processing method using the foregoing numerically-controlled cutting apparatus, although the Y-axis table allows a turning tool to perform a reciprocating fine motion at a high speed in the Y-axis direction since it is small and light and accordingly its inertia force is small, the X-axis table is not capable of allowing the turning tool to perform a reciprocating fine motion at a high speed in the X-axis direction since it is big and heavy and accordingly its inertia force is large.
Hence, when a lens for correcting heavy astigma is cut so as to provide a toric surface or the like having large undulation, the X-axis table cannot follow the number of rotation of a work used in a normal processing operation of a lens. Accordingly, the number of rotation of the work must be reduced to the extent to which the X-axis table can follow, thereby resulting in reduced productivity.
Since the X-axis table is required to move at least over a distance of the radius of a work, there is a limit for making the moving distance of the X-axis table smaller. Also, although an ultra-high-power motor may allow the X-axis table to perform a reciprocating motion at high speed, it is not possible because of large inertia force.